XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #571,412

Block #571,412

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2014, 11:19:37 AM Β· Difficulty 10.9653 Β· 6,225,900 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
8af51a11ce9d6a76de612cb21125ea678bf25173e0fd0c4db6391865efe6f35e
View on Chainz β†—

Height

#571,412

Difficulty

10.965283

Transactions

1

Size

209 B

Version

2

Bits

0af71cca

Nonce

212,602,443

Timestamp

6/1/2014, 11:19:37 AM

Confirmations

6,225,900

Merkle Root

0875e032d9c4b8abcd1b532d0cf9042c9d4338d6bbf7263f1fb7cc15be464aea
Transactions (1)
Coinbase0875e032d9c4b8…b7cc15be464aea
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.236 Γ— 10¹⁰¹(102-digit number)
52367392926630582012…49040451598254080000
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.236 Γ— 10¹⁰¹(102-digit number)
52367392926630582012…49040451598254079999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.236 Γ— 10¹⁰¹(102-digit number)
52367392926630582012…49040451598254080001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.047 Γ— 10¹⁰²(103-digit number)
10473478585326116402…98080903196508159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.047 Γ— 10¹⁰²(103-digit number)
10473478585326116402…98080903196508160001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.094 Γ— 10¹⁰²(103-digit number)
20946957170652232805…96161806393016319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.094 Γ— 10¹⁰²(103-digit number)
20946957170652232805…96161806393016320001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.189 Γ— 10¹⁰²(103-digit number)
41893914341304465610…92323612786032639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.189 Γ— 10¹⁰²(103-digit number)
41893914341304465610…92323612786032640001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
8.378 Γ— 10¹⁰²(103-digit number)
83787828682608931220…84647225572065279999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.378 Γ— 10¹⁰²(103-digit number)
83787828682608931220…84647225572065280001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.675 Γ— 10¹⁰³(104-digit number)
16757565736521786244…69294451144130559999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 571412

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 8af51a11ce9d6a76de612cb21125ea678bf25173e0fd0c4db6391865efe6f35e

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #571,412 on Chainz β†—
Circulating Supply:57,622,517 XPMΒ·at block #6,797,311 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK